Prove the following?

Answer:

The square root of 50 is approximately 7.07.

Answer:

7.07106781187...

Step-by-step explanation:

its an irrational number

The solution to the proportional equation 5/8 = 8/a is a = 64/5 or a = 12.8.

To solve the proportional equation 5/8 = 8/a, we can cross-multiply.

Cross-multiplying means multiplying the numerator of the first fraction by the denominator of the second fraction and vice versa.

We have:

5 × a = 8 × 8

5a = 64

To isolate the variable a, we divide both sides of the equation by 5:

a = 64/5

We may cross-multiply the proportional equation 5/8 = 8/a to find the solution.

Cross-multiplication is the process of multiplying the denominator of the second fraction by the first fraction's numerator, and vice versa.

We possess

5 × a = 8 × 8 5a = 64

We divide both sides of the equation by 5 to identify the variable a:

a = 64/5.

We may cross-multiply to find the solution to the proportional equation 5/8 = 8/a.

Cross-multiplication is the process of multiplying one fraction's numerator by another's denominator and vice versa.

There are:

5 × a = 8 × 8 5a

= 64

By multiplying both sides of the equation by 5, we may separate the variable a:

a = 64/5.

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The option that would create an appropriate strata is given as follows:

Four teachers from each school in the district are chosen at random to complete a survey on the topic.

Samples may be classified as follows:

An appropriate strata is created when stratified sampling is used that is, the population is divided into groups(each school in the district), and then an equal amount(four teachers from each school) is surveyed.

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Answer:

x ≈ 12.7

Step-by-step explanation:

since the triangle is isosceles then the 2 legs are congruent, both 9

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² = 9² + 9² = 81 + 81 = 162 ( take square root of both sides )

x = [tex]\sqrt{162}[/tex] ≈ 12.7 ( to the nearest tenth )

Answer:

Solution is in the attached photo.

Step-by-step explanation:

This question tests on the concept of triangles, as this is an isosceles triangle, the other 2 unknown angles are the same, as well as the sine rule.

Answer:

C

Step-by-step explanation:

[tex]9\sqrt{x} + 3\sqrt{3x} + \sqrt{9x} \\= \sqrt{x} ( 9 + 3\sqrt{3}+3)\\ = 12\sqrt{x} + 3\sqrt{3x}[/tex]

The ratio that represents Stefan's share is given as follows:

5/14.

Roman is the person that will get more money.

The shares are obtained applying the proportions in the context of the problem.

Stefan and Roman share some money in the ratio 5:9, hence the denominator of the fraction is given as follows:

5 + 9 = 14.

Then the shares are given as follows:

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.1.1(2-√√-225) = 2.1.1(2-15) = 2.1.1(-13) = -27.31

To solve this problem, we first need to simplify the expression inside the parentheses. The square root of a negative number is an imaginary number, so we can write the expression as follows:

2.1.1(2-√-225) = 2.1.1(2-√(-1)(225))

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We can then simplify the expression as follows:

2.1.1(2-√(-1)(225)) = 2.1.1(2-i*15) = 2.1.1(2-15) = 2.1.1(-13) = -27.31

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The second problem is a bit more complicated. We need to use the fact that the square root of a negative number is an imaginary number. We can write the expression as follows:

3+√-18 = 3+√(-1)(18)

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We can then simplify the expression as follows:

3+√(-1)(18) = 3+i*3 = 3+3i

Answer:

A = 30 cm

B = 14 cm

C = 15 cm

D = 41 cm

Step-by-step explanation:

You can find A by multiplying 10 times 6 (because the other side of the square is ten and the side of A already has that 4 there it would be 6) which would be 60, then since it is a right triangle, you can divide that by two and get 30.

You can find B by multiplying 4 by 7 (because the other part of that side of the square is 3 so that part would be 7) which would be 28, then since it is a right triangle, you can divide that by two and get 14.

You can find C by multiplying 10 times 3 and getting 30, then since it is a right triangle, you can divide that by two and get 15.

You can find D by multiplying 10 by 10 (because it is a square) then you'll get 100 from that. Then you can subtract the rest of the triangles from it which would be 100 minus 30 minus 14 minus 15 and you would get 41 which would be triangle D.

Hope this helps!! Let me know if you need more explanation

The passing score cutoff is 39, and 22.22% of the students failed.

Using the generic formula =

Z = score - mean / standard deviation

According to the question, the results of a psychology test had a mean of 57 and a standard deviation of 9, and they were normally distributed.

Anything 2 or more standard deviations below the mean on the test was considered a failing grade,

hence z = 2/9 = 0.222.

Additionally, the falling cut-off score is determined by using the formula: Falling cut-off = mean - 2 x standard deviation,

or 57 - 2 x 9 = 39.

Hence the passing score cutoff is 39, and 22.22% of the students failed.

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Answer:

Step-by-step explanation:

lets solve all the equations and check:

1 ) 8 - x = 11

 -x = 11 - 8

  x = -3 ------------- not this one

2 ) x + 7 = 4

    x = 4 - 7

    x = -3 -------------not this one

3 ) 5 + x = 9

    x = 9 - 5

    x = 4 ------------- not this one

4 ) x - 2 = 1

    x = 1 + 2

    x = 3 ----------- this is the correct option

                hope this helps!

The minimum of this quadratic function is -55.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:

Axis of symmetry, Xmax = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function T = n²- 10n - 30, we have:

Axis of symmetry, Xmax = -(-10)/2(1)

Axis of symmetry, Xmax = 10/2 = 5.

For the vertex of T = n²- 10n - 30, we have:

T = n²- 10n - 30

T(5) = 5²- 10(5) - 30

T(5) = -55.

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Answer:

16 and 4

Step-by-step explanation:

To divide 20 in the ratio 4:1, we need to divide the quantity into 5 parts (4 parts for the first ratio and 1 part for the second ratio) and then allocate the parts accordingly.

The total number of parts is 4+1=5. So, each part represents 20/5 = 4.

To find the share of the first ratio, we multiply the first ratio (4) by the number of parts it represents (4). So, the first share is 4*4 = 16.

To find the share of the second ratio, we multiply the second ratio (1) by the number of parts it represents (1). So, the second share is 1*4 = 4.

Therefore, the quantities in the ratio 4:1 that add up to 20 are 16 and 4, respectively.

The solution is; C. x² + 2x - 1 = 3 equation could be solved using this application of the quadratic formula.

Here,

Quadratic formula: x = -b±√b²-4ac/2a     [ +/-   is   ± ]    

You can find the value of a, b, c  -->  ax² + bx + c = 0  

we have,

x = -2±√2² - 4×1× -4 / 2×1    

Since this is not simplified, you can find a, b, c:

a = 1

b = 2

c = -4

A.)  x² + 1 = 2x − 3   Make the equation into ax² + bx + c = 0.

Subtract 2x on both sides, and add 3 on both sides to set the equation equal to 0

x² + 1 - 2x + 3 = 2x - 2x - 3 + 3

x² - 2x + 4 = 0      

a = 1

b = -2

c = 4    This is not the answer because b = 2 not -2, and c = -4 not 4

B.) x² - 2x − 1 = 3     Subtract 3 on both sides to set the equation = 0

x² - 2x - 4 = 0

a = 1

b = -2

c = -4      This is not the answer because b = 2 not -2

C. x² + 2x - 1 = 3    Subtract 3 on both sides to set the equation = 0

x² + 2x - 4 = 0

a = 1

b = 2

c = -4    This is your answer

D. x² + 2x - 1 = -3      Add 3 on both sides to set the equation = 0

x² + 2x + 2 = 0

a = 1

b = 2

c = 2    

This is not the answer because c = -4 not 2

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complete question:

Which equation could be solved using this application of the quadratic formula?

x = -2±√2² - 4×1× -4 / 2×1    

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 5.6\%\to \frac{5.6}{100}\dotfill &0.056\\ t=years\dotfill &3 \end{cases} \\\\\\ A = 500[1+(0.056)(3)] \implies A=500(1.168)\implies A = 584[/tex]

Answer:

Answer:

I = $ 84.00

Calculation:

First, converting R percent to r a decimal

r = R/100 = 5.6%/100 = 0.056 per year,

then, solving our equation

I = 500 × 0.056 × 3 = 84

I = $ 84.00

The simple interest accumulated

on a principal of $ 500.00

at a rate of 5.6% per year

for 3 years is $ 84.00.

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

The variables in this problem are classified as follows:

In the context of this problem, the number of siblings is the only discrete variable, as is the only variable that cannot assume decimal values.

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Answer:

The fraction of cupcakes they ate is:

5 / 8

The fraction of cupcakes left is:

3 / 8

Answer:

You dont have to tell me to show my work twice

Step-by-step explanation:

To find the length of side c (the hypotenuse), we will use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (a and b) is equal to the square of the hypotenuse (c).

In this case, a = 30 feet and b = 40 feet. Therefore:

c^2 = a^2 + b^2

c^2 = 30^2 + 40^2

c^2 = 900 + 1600

c^2 = 2500

c = √2500

c = 50 feet

So the length of side c (the hypotenuse) is 50 feet. To find out how many feet of flowers will be planted along side c, we need to know the perimeter of the triangle (the sum of the lengths of all three sides). The perimeter is:

Perimeter = a + b + c

Perimeter = 30 + 40 + 50

Perimeter = 120 feet

Therefore, 120 feet of flowers will be planted along side c.

Answer:   Here, side a = 30ft.

side b = 40ft.

Hence according to, Pythagoras theorem,

h²=p²+b²

where, h= hypotenuse of the triangle

            b= base of the triangle

            p= perpendicular of the triangle

Step-by-step explanation:

hypotenuse c {according to question} - c=[tex]\sqrt{a^{2} + b^{2}[/tex]

therefore, c=[tex]\sqrt{30^{2} + 40^{2} }[/tex] = 50ft. will be the answer.

Hypotenuse means the longest side of the triangle or in other words the side opposite to the 90° angle of the triangle.

The domain of the function (t) in h = - 16t² + 56t should be greater than

or equal to 43.5 seconds as the height of the rocket can not be negative.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given that;

A rocket is launched into the air. Its height in feet is given by

h = - 16t² + 72t.

Where t represents time in seconds and h represents the height in feet.

We know that height can not be negative.

h ≥ 0.

So,  - 16t² + 56t ≥ 0.

- 16t² ≥ -56t.

16t² ≥ 56t.

16t ≥ 56.

t ≥ 56/16.

t ≥ 3.5 seconds.

Therefore, the domain of the function (t) in h = - 16t² + 56t should be greater than or equal to 3.5 seconds.

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The 97% confidence interval for the proportion of college freshmen who would report cheating if they witnessed it in class is (0.0728, 0.1482).

The point estimate is the proportion of students who responded "yes" out of the total sample.

In this case, the point estimate is 19/172, which is approximately 0.1105.

b. Margin of Error:

To calculate the margin of error, we need the standard deviation. Since we don't have the population standard deviation, we'll use the formula for the estimated standard deviation of a proportion:

Margin of Error (ME) = z√[(p(1 - p)) / n]

Where z is the z-score corresponding to the desired confidence level. For a 97% confidence level, the z-score is approximately 1.96, p is the point estimate of the proportion and n is the sample size.

Using the given values, we can calculate the margin of error:

ME = 1.96√[(0.1105(1 - 0.1105)) / 172]= 0.0377

c. Confidence Interval:

The confidence interval is calculated by subtracting and adding the margin of error from the point estimate.

Confidence Interval = Point Estimate ± Margin of Error

Confidence Interval = 0.1105 ± 0.0377

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Answer:

3.6

Step-by-step explanation:

Sine rule:   a/SIN A  =  b/SIN B  =   c/SIN C.

right-angled triangle, so angle N = 90°.

x/sin 32  = 6.8/sin 90

x = (6.8 X sin 32) / sin 90

= 3.6

The probability of getting at one hit is 2/5

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 which is equivalent to 100%

Probability = sample space / total outcome

The sample space of getting at least 1 hit.

is 4.

Total outcome = 10

probability to get at least one hit = 4/10

= 2/5

Therefore the probability of getting atleast one hit is 2/5

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The proportion that correctly defines θ is BC/PC = DE/PE = θ.

option  C.

The length of the arcs is calculated as follows;

Length of arc = (θ/360) x 2πr

where;

For sector PCB, the length of the arc is given as;

(θ/360) x 2π(PC) = BC

(θ/360) x 2π = BC/PC

θ = BC/PC ------- (1)

Note: 2π radian = 360⁰

For sector PED, the length of the arc is given as;

(θ/360) x 2π(PE) = DE

(θ/360) x 2π = DE/PE

θ = DE/PE ------- (2)

Compare the two equations as follows;

BC/PC = DE/PE = θ

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Answer:

The original number was 4.

Step-by-step explanation:

We can construct an equation to model the given situation, using a variable x to represent the original number:

"the quantity of 6 minus a number"

[tex](6 - x)[/tex]

"four times the quantity"

[tex]4(6 - x)[/tex]

"is 8"

[tex]4(6 - x) = 8[/tex]

We can solve for x in this equation.

[tex]4(6 - x) = 8[/tex]

↓ applying the distributive property ... [tex]A(B+C) = AB + AC[/tex]

[tex]24 - 4x = 8[/tex]

↓ adding 4x to both sides

[tex]24 = 8 + 4x[/tex]

↓ subtracting 8 from both sides

[tex]16 = 4x[/tex]

↓ dividing both sides by 4

[tex]4 = x[/tex]

[tex]\boxed{x = 4}[/tex]

So, the original number was 4.

The points that are solutions to the equation [tex]2x^2 + y = 4[/tex] are:

I. (3, -14)

III. (-3, -14)

To determine which of the given points are solutions to the equation [tex]2x^2 + y = 4[/tex], we need to substitute the x and y values of each point into the equation and check if the equation holds true.

Let's evaluate each point one by one:

I. (3, -14)

Substituting x = 3 and y = -14 into the equation:

[tex]2(3)^2 + (-14) = 4[/tex]

18 - 14 = 4

4 = 4

Since both sides of the equation are equal, the point (3, -14) is a solution to the equation.

II. (-3, 14)

Substituting x = -3 and y = 14 into the equation:

[tex]2(-3)^2 + 14 = 4[/tex]

18 + 14 = 4

32 = 4

Since the equation is not satisfied (32 is not equal to 4), the point (-3, 14) is not a solution to the equation.

III. (-3, -14)

Substituting x = -3 and y = -14 into the equation:

[tex]2(-3)^2 + (-14) = 4[/tex]

18 - 14 = 4

4 = 4

Since both sides of the equation are equal, the point (-3, -14) is a solution to the equation.

In summary, the points that are solutions to the equation [tex]2x^2 + y = 4[/tex]are:

I. (3, -14)

III. (-3, -14)

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hello

the answer to the question is:

y = a tan(bx – c) + d

a = 1, b = 1, c = π/2

the midline is y = d, so y = 0 and there's no vertical shift

the vertical stretch is 1, so label the y-axis so the inflection point of the curve is 1 above the midline, 1, and the other inflection point is 1 below the midline, −1

the period is:

T = π/b ----> T = π

the phase shift is:

PS = c/b ----> PS = π/2

and also, there's no amplitude for tangent and cotangent, there is only the vertical stretch that takes the place of an amplitude

Answer:

.343656

Step-by-step explanation:

e-5x+1=2

Subtract the 1 to the other side.

e-5x=1

Subtract e to the other side (e is approximately 2.718)

-5x=-1.718

Divide by -5.

x=.343656

Answer:

y = - 3x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, - 5 ) and (x₂, y₂ ) = (3, - 2 )

m = [tex]\frac{-2-(-5)}{3-4}[/tex] = [tex]\frac{-2+5}{-1}[/tex] = [tex]\frac{3}{-1}[/tex] = - 3 , then

y = - 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, - 2 )

- 2 = - 3(3) + c = - 9 + c ( add 9 to both sides )

7 = c

y = - 3x + 7 ← equation of line

The true statement is that the box-plot indicates that:

To determine the validity of this statement, we compare the minimum weekly salary of men (represented by the lower end of the box-plot whisker) to the median of women's earnings (represented by the line inside the box).

If the median of women's earnings is less than the minimum salary of men, then more than 50% of women earn less than the minimum weekly salary of men.

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